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andriy [413]
2 years ago
10

If a two digit number has x for a tens digit and a units digit that is 3 more than x. What is the value of the number in terms o

f x ?
Mathematics
1 answer:
Arada [10]2 years ago
7 0

The value of the number in terms of x will be : 11x + 3

Explanation:

In the two digit number tens' digit is x and units' digit is 3 more than x , that means (x+3)

For getting a number, we will first multiply each digit by it's position and then just add all the products.

For x, the position is 10 and for (x+3), position is unit i.e. 1

So, the number will be:

[x*10]+[(x+3)*1] \\ \\ =10x + x+3\\ \\ =11x+3

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A company that rents small moving trucks wants to purchase 25 trucks with a combined capacity of 28,000 cubic feet. Three differ
pickupchik [31]

Answer:

We have 4 solutions:

  • No 10-foot truck, 10  14-foot trucks, and 15 24-foot trucks
  • 2 10-foot trucks, 7 14-foot trucks, and 16 24-foot trucks
  • 4 10-foot trucks, 4  14-foot trucks, and 17 24-foot trucks
  • 6 10-foot trucks, 1 14-foot trucks, and 18 24-foot trucks

Step-by-step explanation:

Let the number of 10-foot truck with a capacity of 350 cubic feet purchased=a

Let the number of 14-foot truck with a capacity of 700 cubic feet purchased=b

Let the number of 24-foot truck with a capacity of 1,400 cubic feet purchased=c

The company wants to purchase 25 trucks, therefore.

  • a+b+c=25

Furthermore, the combined capacity of the trucks is 28,000 cubic feet.

  • 350a+700b+1400c=28000

Since the number of equations is less than the number of variables, you can not use a matrix equation to solve this problem.  The solution is most easily found using an augmented matrix.  

The augmented matrix is presented below:  

\left[\begin{array}{ccc|c}1&1&1&25\\350&700&1400&28000\end{array}\right]

Using the calculator, the reduced row echelon form is:

\left[\begin{array}{ccc|c}1&0&-2&-30\\0&1&3&55\end{array}\right]

where  

a- 2c=-30 means a =2c-30

b+3c=55 means b= 55-3c

We alter the value of c as long as neither a nor b becomes negative. Suitable values for c are 15, 16, 17, and 18:

\left|\begin{array}{|c||c||c|}a=2c-30&b=55-3c&c\\0&10&15\\2&7&16\\4&4&17\\6&1&18\end{array}\right|

We can easily  verify that, for each solution, the number of trucks adds up to 25 and the fleet capacity is 28,000 cubic feet.

We therefore have 4 solutions:

  • No 10-foot truck, 10  14-foot trucks, and 15 24-foot trucks
  • 2 10-foot trucks, 7 14-foot trucks, and 16 24-foot trucks
  • 4 10-foot trucks, 4  14-foot trucks, and 17 24-foot trucks
  • 6 10-foot trucks, 1 14-foot trucks, and 18 24-foot trucks
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A pizza parlor offers a choice of 12 different toppings. How many 4-topping pizzas are possible? (no double orders of toppings a
Serhud [2]
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3 years ago
What is the quotient?
Ugo [173]

Answer:

I got 4e+12 which is d

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Step-by-step explanation:

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3 years ago
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Solve for b. b + (-42) = -86
blsea [12.9K]

Answer:

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Step-by-step explanation:

beacuse Yan ang answer

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3 years ago
Find the mean of each distribution.
Vanyuwa [196]

Answer:

a) 23 °C

b) 5.81 m² (2 dp)

Step-by-step explanation:

<h3><u>Part (a)</u></h3>

This set of data is presented as a <u>Dot Plot</u>.

The frequency (how often a data value occurs) is represented by the number of dots above each data value.

For example, in this dot plot, there are 3 dots above the data value 21 °C and so this means that there are three of this particular data value in the set of data.

To find the mean, we need to multiply each data value by its frequency, add them up, then divide by the total frequency.

\begin{aligned}\textsf{mean}&=\dfrac{3 \times 21+1 \times 22+2\times 23+5\times 24+1\times 25}{3+1+2+5+1}\\\\ & = \dfrac{63+22+46+120+25}{12}\\\\& = \dfrac{276}{12}\\\\&=23^{\circ} \sf C\end{aligned}

<h3><u>Part (b)</u></h3>

This set of data is presented as a <u>stem and leaf diagram</u>, where the units and tenths are split.  The units column is the 'stem' and the tenths become the 'leaf'.

Therefore, the first row of this stem and leaf diagram represents 2 data values: 4.3 and 4.8

To find the mean, sum the data values, then divide by the total frequency.

To find the total frequency, simply count the number of values in the leaf part of the diagram.

Data values = 4.3, 4.8, 5.1, 5.1, 5.2, 5.5, 5.7, 6.6, 6.9, 7.3, 7.4

Total frequency = 11

\begin{aligned}\textsf{mean} &=\dfrac{4.3 + 4.8 + 5.1+5.1+5.2+5.5+5.7+6.6+6.9+7.3+7.4}{11}\\ & = \dfrac{63.9}{11}\\\\& = 5.81\:\textsf{(2 dp)}\end{aligned}

4 0
1 year ago
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